Math, asked by atharva7143, 11 months ago

If alpha + beta = 5 and alpha^3+beta^3= 35, find the quadratic equation whose roots are Alpha and beta

Answers

Answered by anuanku

Answer:

it is given that,

α + β = 5 and α³ + β³ = 35

then we have to find the quadratic equation whose roots are α and β.

as α³ + β³ = 35

⇒(α + β)³ - 3αβ(α + β) = 35

⇒(5)³ - 3αβ(5) = 35

⇒125 - 35 = 15αβ

⇒90 = 15αβ

⇒αβ = 6

now, quadratic equation is given

x² - (sum of roots)x + product of roots

⇒x² - (α + β)x + αβ

⇒x² - 5x + 6

Answered by MagicalGiggles

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Given

➡️alpha + beta = 5

➡️alpha³ + beta³ = 35

[ use formula ]

♦️( a + b )³ = a³ + b³ + 3ab ( a + b )

let

⚡a = alpha

⚡b = beta

➡️( alpha + beta )³ = alpha³ + beta³ + 3.alpha.bera ( alpha + beta )

[ substitute the above values in above formula ]

⭐( 5 )³ = 35 + 3.alpha.beta ( 5 )

⭐125 = 35 + 3.alpha.beta ( 5 )

⭐125 - 35 = 3.alpha.beta ( 5 )

⭐90 = 3.alpha.beta ( 5 )

⭐alpha × beta = 6

➡️➡️➡️➡️➡️The quadratic equation is x² - ( alpha + beta )x + alpha × beta

:. x² - 5x + 6

$<marquee>♦️DULARI♦️</marquee>$

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